341review-part2 - Math 341 Review Fall 2010 2. Linear...

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Unformatted text preview: Math 341 Review Fall 2010 2. Linear algebra This topic covered parts of Chapters 1, 2, 3, and 6 of the Leon book. A good way to review is to do particular problems. 1. Solve the following systems or show that they are inconsistent. 1a. x 1- 2 x 2 = 5 3 x 1 + x 2 = 1 1b. 4 x 1 + 3 x 2 = 4 2 3 x 1 + 4 x 2 = 3 1 1c. 2 x 1- 3 x 2 = 5- 4 x 1 + 6 x 2 = 8 1d. x 1 + x 2 = 0 2 x 1 + 3 x 2 = 0 3 x 1- 2 x 2 = 0 1e. 2 x 1 + 3 x 2 + x 3 = 1 x 1 + x 2 + x 3 = 3 3 x 1 + 4 x 2 + 2 x 3 = 4 2 2. Compute the following determinants (using whatever method you think is most appropriate). 2a. 3 1 2 2 5 4 2 5 4 2b. 1 3 2 4 1- 2 2 1 3 2c. 2 0 0 1 0 1 0 0 1 6 2 0 1 1- 2 3 3 3. Find all possible values of c that would make the matrix nonsingular: 1 1 1 1 9 c 1 c 3 4. Which of the following are spanning sets for R 3 ? 4a. (1 , , 0) T , (0 , 1 , 1) T , (1 , , 1) T , (1 , 2 , 3) T 4b. (2 , 1 ,- 2) T , (3 , 2 ,- 2) T , (2 , 2 , 0) T 4 5. Which of the following sets are linearly independent in R 3...
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This note was uploaded on 12/07/2011 for the course MATH 341 taught by Professor Zhang during the Fall '08 term at University of Delaware.

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341review-part2 - Math 341 Review Fall 2010 2. Linear...

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